   Theorem 2.7 [1]}
Let  \(\left\lbrace \,f_{\,i}\,\right\rbrace _{i \,=\, 1}^{\infty }\)  be a sequence in  \(H\)  and  \(B \,>\, 0\)  be given.Then  \(\left\lbrace \,f_{\,i}\,\right\rbrace _{i \,=\, 1}^{\infty }\)   is a Bessel sequence with Bessel bound  \(B\)   if and only if the operator defined by \( T \,:\, l^{\,2}\,(\,\mathbb {N}\,) \,\rightarrow \, H,\; T\,\lbrace \,c_{i}\,\rbrace  \,=\, \sum \limits _{i \,=\, 1}^{\infty } \;c_{\,i}\,f_{\,i}\) 
is bounded and \(\Vert \,T\,\Vert  \,\le \, \sqrt{B}\) .

